
theorem
  for G being _Graph, E being one-to-one ManySortedSet of the_Edges_of G
  for W2 being Walk of replaceEdges(E) ex W1 being Walk of G
  st W1.vertexSeq() = W2.vertexSeq() & E*(W1.edgeSeq()) = W2.edgeSeq()
proof
  let G be _Graph;
  let E be one-to-one ManySortedSet of the_Edges_of G;
  let W2 be Walk of replaceEdges(E);
  consider W1 being Walk of G such that
    A1: (id the_Vertices_of G)*(W1.vertexSeq()) = W2.vertexSeq() and
    A2: E*(W1.edgeSeq()) = W2.edgeSeq() by Th21;
  take W1;
  rng(W1.vertexSeq()) c= the_Vertices_of G;
  hence thesis by A1, A2, RELAT_1:53;
end;
